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Lecture NotesASTR 1000Fall 2009Slide Set 1Celestial MotionsDr. H.A. McAlisterDept. of Physics AstronomyGeorgia State Un - PowerPoint PPT Presentation


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Lecture Notes ASTR 1000 Fall 2009 Slide Set #1 Celestial Motions Dr. H.A. McAlister Dept. of Physics & Astronomy Georgia State University. The Constellations.

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Lecture Notes

ASTR 1000

Fall 2009

Slide Set #1

Celestial Motions

Dr. H.A. McAlister

Dept. of Physics & Astronomy

Georgia State University


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The Constellations

  • 88 constellations in the sky. Those in the northern celestial hemisphere named by the Greeks. Constellations in the extreme southern sky were named in modern times.

  • Subsets of constellations are called asterisms. For example, the “Big Dipper” is an asterism of the constellation Ursa Major (the big bear).

  • While constellations were named by the Greeks, Arabic names have been mostly adopted for individual stars. Stars within a constellation are assigned Greek letters in accordance with their brightest. For example, the brightest star in Orion has the Arabic name Betelgeuse, but it is also known as a Orionis. Orion’s second brightest star, Rigel, is also called b Orionis.

  • The twelve constellations lying along the projection of the Earth’s orbit onto the sky (the ecliptic) comprise the zodiac.


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Winter Sky – Facing North


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Winter Sky – Facing South


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Orion

as Depicted by

J. Hevelius

(1690)

(Note that this is as

viewed from outside

celestial sphere)


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Spring Sky – Facing North


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Spring Sky – Facing South


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Celestial Motions

  • The rotation of the Earth about its spin axis once every 24 hours causes diurnal effects including day and night and the rising and setting of celestial objects.

  • The revolution of the Earth about the sun once every 365.2422… days produces annualeffectssuch as the sun appearing to move with respect to the stars along a path in the sky called the ecliptic. The twelve constellations lying along the ecliptic comprise the zodiac.

  • The apparent motions of celestial objects on the sky are the combined result of diurnal and annual motions and, in the case of the planets their own orbital motions around the sun.


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The Celestial Sphere

north celestial pole

Earth’s

spin

axis

north pole

equator

celestial equator

south pole

celestial

sphere

south celestial pole


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Terrestrial Coordinates

N

* Greenwich

* Atlanta

latitude

Equator

longitude

S

For Atlanta:

latitude = 33o 45’ N

longitude = 84o 23’ W


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Lunar Months

All motions are counterclockwise

Time from t1 to t2 is the “sidereal month”

(This is time required for realignment

with respect to the stars and equals 27.3 days.)

t1

Time from t1 to t3 is the “synodic month”

(This is the time between repetition of phases

and equals about 29.5 days. This is what we

use for our calendar.)

t2

t3


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Lunar Phases

first

quarter

waxing

gibbous

waxing

crescent

sunlight

sunset

full

moon

new

moon

noon

midnight

to the Sun

sunrise

Earth

waning

gibbous

waning

crescent

sunlight

third

quarter


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Questions About Lunar Phases

  • What is the time interval between new and full moons?

  • What time does the full moon culminate?

  • What time does the new moon culminate?

  • What time does the new moon rise?

  • What is the phase of the moon that culminates at sunset?

  • What is the phase of the rising moon at sunset?

  • What is the phase of the setting moon at midnight?

two weeks

midnight

noon

sunrise

first quarter

full

first quarter


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“Earthshine”

waxing

crescent

Moon

Sunlight reflected off day lit side of Earth

illuminates dark part of crescent moon.

sunlight

to the Sun

Earth

The effect is most obvious just before and

just after new moon

sunlight


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The Tides

4. On the far side, the Earth is effectively pulled Moonward away from the water, yielding another high tide.

3. The water on the near side of the Moon is pulled away from Earth, raising a high tide.

Earth

Moon

2. The presence of the Moon produces a gravitational attraction on the Earth whose strength varies inversely with distance from the Moon.

1. Imagine a perfectly spherical Earth uniformly flooded by an ocean.


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Moon Factoids

  • A “blue moon” is when more than one full moon occurs in the same calendar month.

  • The moon undergoes “synchronous” rotation and revolution (i.e. the periods of rotation and revolution are identical), so one side of the moon always faces the Earth.

  • The “harvest moon” involves the rising of the full moon in late September and early October. Due to the angular tilt of the moon’s orbital plane with that of the Earth, the bright moon appears to rise at about the same time in the early evening when the moon is full at the time of the “autumnal equinox”.


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Moon Myths

  • The phase of the moon has no effect on human behavior.

  • There is no such thing as the “dark side of the moon.”

  • We did indeed land humans on the moon in the six Apollo landings between July 1969 and December 1972.

  • For more about “lunatics”, the “moon hoax” and other astronomical pseudoscience, see:

  • www.astrosociety.org/education/resources/pseudobib.html


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Tilt of Earth’s Spin Axis

23.5o tilt

The Earth’s spin axis is tilted by 23.5 degrees off vertical with respect to

the “ecliptic plane” (plane of the Earth’s orbit around the sun)

The spin axis remains essentially parallel to itself during the course of the year


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Summer Solstice – 21 June

tropic of

Cancer

arctic

circle

sunlight

equator

antarctic

circle

sunlight


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Winter Solstice – 21 December

tropic of

Cancer

arctic

circle

sunlight

equator

antarctic

circle

sunlight

tropic of

Capricorn


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Vernal Equinox – 21 March

arctic

circle

sunlight

tropic of

Cancer

equator

tropic of

Capricorn

sunlight

antarctic

circle


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Autumnal Equinox – 21 September

arctic

circle

sunlight

tropic of

Cancer

equator

tropic of

Capricorn

sunlight

antarctic

circle


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The Culminating Sun

  • The sun culminates in the zenith (i.e. straight overhead) at noon for observers located on the tropic of Cancer (latitude = 23.5o N) on the day of the summer solstice.

  • The sun culminates in the zenith at noon for observers located on the tropic of Capricorn (latitude = 23.5o S) on the day of the winter solstice.

  • The sun culminates in the zenith (i.e. straight overhead) at noon for observers located on the equator (latitude = 0o) on the days of the equinoxes.


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Other Seasonal Extremes

  • The sun never rises for observers north of the arctic circle on the day of the winter solstice

  • The sun never sets for observers north of the arctic circle on the day of the summer solstice

  • The above conditions are reversed for the antarctic circle.

  • The sun moves 360o around the horizon for observers located at the north and south poles on the days of the equinoxes.


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Tilt of Earth’s Spin Axis

W

N

S

E

winter

solstice

summer

solstice

equinox

The sun rises on the east point and sets on the west point on the days of the equinoxes, giving

equal periods of “day” and “night”.

The sun is in the sky for the longest duration on the summer solstice and illuminates

the northern hemisphere most directly.


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Temperature Effect

  • Summer days are longer and the sun is more intense (due to the more direct illumination angle). Thus summer is hotter than winter.

  • There is a lag of the seasons when comparing the dates of the solstices with the actual extremes in temperature because it takes time to heat up the oceans and atmosphere at the onset of summer and to cool them off at the onset of winter.

  • If the Earth’s spin axis were not tilted by some angle, we would have no seasons.


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Precession of Earth’s Spin Axis

5. Spin axis now points to Polaris. 13,000 years from now, Vega will be our “pole star”

4. Earth responds to this pull by slowly “precessing” its spin axis around a circle in the sky once every 26,000 years

23.5o

2. Moon’s orbital plane is tilted by 5o from our equator

3. Moon’s gravitational pull on Earth attempts to pull bulge into lunar orbital plane

1. The rotation of the Earth distorts it into an “oblate” spheroid flattened at the poles


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Shadows and Eclipses

Sun

Penumbra

Umbra

Earth


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Eclipse of the Moon (Lunar Eclipse)

Earth’s Orbit

Moon’s Orbit

Occurs at Full Phase when Moon is also at the “line of nodes” of its orbit

with respect to the ecliptic

A lunar eclipse lasts for many hours and can be seen from the majority of the

Earth’s surface


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Eclipse of the Sun (Solar Eclipse)

Earth’s Orbit

Moon’s Orbit

Occurs at New Phase when Moon is also at the “line of nodes” of its orbit

with respect to the ecliptic

A solar eclipse lasts for only for a few minutes and can only be seen from very restricted

locations on the Earth’s surface


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Total and Annular Eclipses

Vertex of Umbral shadow is at or below Earth’s surface, so a total eclipse is possible

Vertex of Umbral shadow is above Earth’s surface, so only an annular eclipse is possible


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Example of a Solar Eclipse Path

See Richard Monk’s

webpage on eclipses:

www.williams.edu/

astronomy/IAU_eclipses/


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Total Solar Eclipse of 21 June 2001 from Zimbabwe

See Richard Monk’s

webpage on eclipses:

www.williams.edu/

astronomy/IAU_eclipses/

Bailey’s Beads

Solar Corona

“Diamond Ring”


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Upcoming Lunar and Solar Eclipses

Solar Eclipses:

15 Jan 2009 (annular) – Asia & Africa

11 July 2010 (total) – South Pacific Ocean

4 Jan 2011 (partial) – Europe, Africa & central Asia

1 Jun 2011 (partial) – east Asia, far N. America, Iceland

1 Jul 2011 (partial) – south Indian Ocean

25 Nov 2011 (annular) – south Africa, Antactica, Tasmania, New Zealand

The next total solar eclipses visible from the U.S. will be on 21 Aug 2017 and

8 Apr 2024. The 2017 eclipse will be visible from Georgia.

Lunar Eclipses:

31 Dec 2009 – not U.S.

15 Jan 2010 (annular) – not U.S.

26 Jun 2010 (partial) – not U.S.

21 Dec 2010 (total) – all U.S.

15 Jun 2011 (total) – not U.S.

10 Dec 2011 (total) – all U.S.


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Motions of the “Wanderers” – The Planets

retrograde motion

normal “direct” (eastward) motion

Mars

East

West

The night sky facing south


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The Geocentric Explanation

All motions are circular

direct

Epicycle moves at constant angular rate about the equant

epicycle

Mars

retrograde

Adjustable parameters include diameters of epicycle & deferent, distance of equant from deferent center, and rates of motion along epicycle & deferent

stationary Earth

.

+

equant

deferent

center

deferent

Developed in detail around 140 AD by Claudius Ptolemy and very successfully used for 1500 years!


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The Heleocentric Explanation

direct motion

retrograde motion

around “opposition”

Sun

direct motion

Earth

Mars

First proposed in detail by Nicolaus Copernicus in ~1505 but not published until De Revolutionibus in 1543.


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Oppositions of Mars

“Favorable”

Opposition

Earth is at aphelion

closest approach is

34 million miles

Mars is at perihelion

“Unfavorable”

Opposition

Earth is at perihelion

closest approach is

68 million miles

Mars is at aphelion

Oppositions of Mars occur at 26-month intervals

On 27 Aug 2003, Mars had its most favorable opposition in 73,000 years


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Orbital Configurations

for an Inferior Planet

Maximum Eastern

Elongation

Inferior

Conjunction

Superior

Conjunction

Earth

Sun

Maximum Western

Elongation


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Orbital Configurations

for a Superior Planet

Eastern Quadrature

Opposition

Earth

Conjunction

Sun

Western Quadrature


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Giants of the Heliocentric Theory

  • Nicolaus Copernicus (1473-1543) – Developed the Heliocentric Theory but waited until just before his death to release his great book, De Revolutionibus.

  • Tycho Brahe (1546-1601) – Greatest pre-telescopic observer, produced extensive observations of Mars that were critical to proving the Heliocentric Theory.

  • Johannes Kepler (1571-1630) – Hired as Tycho’s assistant but only gained access to Tycho’s complete data after Tycho’s premature death. Kepler discovered three “laws of planetary motion” that revolutionized the understanding of the solar system.

  • Galileo Galilei (1564-1642) – First used the telescope for observing the night sky in 1609. His discoveries were monumental and included proof of the Heliocentric Theory.

  • Isaac Newton (1642-1727) – Developed the Law of Universal Gravitation and three laws of motion that completely explain Kepler’s Laws of Planetary Motion.


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Kepler’s First Law

Planets revolve around the sun in elliptical orbits with the sun located at one focus of the ellipse

planet

sun

+

center

focus

focus


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Kepler’s Second Law

The line from the sun to a planet sweeps out equal areas in equal time intervals.

t1

areaA

t2

t4

aphelion

(slowest)

perihelion

(fastest)

areaB

areaA = areaB if t2-t1 = t4-t3

t3


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Kepler’s Third Law

For any two planets, the ratio of their mean distance from the sun cubed equals the ratio of their orbital periods squared.

(D1/D2)3 = (P1/P2)2

Planets far from the sun take longer to orbit the sun than do planets nearer the sun.


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Galileo’s Telescopic Discoveries

  • New Stars – Discovered that his telescopes revealed far more stars than are accessible to the unaided eye.

  • Lunar Feature – Found the moon to have craters, mountains and complicated terrain. He also reported spots on the sun, although it turns out they had first been reported centuries earlier by Chinese astronomers.

  • Rings of Saturn – Galileo reported that Saturn had “ears” as his telescopes couldn’t quite make out the true nature of the rings.

  • Satellites of Jupiter – Discovered four large moons of Jupiter (still often referred as the “Galilean satellites”) which clearly orbited Jupiter and contradicted the geocentric premise that all bodies move around the Earth.

  • Phases of Venus – He discovered that Venus exhibited a complete cycle of phases, which it could not do under the constraints of the geocentric theory. This was proof of the heliocentric theory.


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